Note: At some point during installation, a screen may come up in your terminal asking if you want to share information about public Go packages you install with the developers. Feel free to answer this question however you want.

Mount your Nexus 7 or whatever using this command after plugging it into your USB port:

go-mtpfs ~/MyAndroid &

When you are finished, unmount your device by using this command:

fusermount -u ~/MyAndroid

I would also like to thank James Gifford for pointing this article out to me on Google+. ;)

In contrast to all the other answers I would still claim that it's not yet possible at all. The question is clearly about "Nexus 7 running Ubuntu" and as far as I understand there is no special service in this first Ubutu port for the Nexus 7 that acts as a USB device. I have a Nexus 7 running Ubuntu here and didn't succeed with any of these solutions mentioned.